Rimfires just can't take the pressure.
In order to throw a 100- to 200-grain bullet fast enough to deliver a striking blow at extreme range, a cartridge must burn enough high-energy (smokeless) powder to raise internal barrel pressures to extreme levels. The .300 Wthby. Mag. blasts up to 65,000 pounds per square inch (psi) of peak pressure. So does the .270 Win. and, surprisingly, the little .22-250 Rem..
In contrast, the .22 Long Rifle tops out at 24,000 psi. This is enough to push a 40-grain bullet about 1,250 fps, enough speed to generate about 130 foot-pounds (fp) of energy at the muzzle. The .22-250 Rem. pushes a 40-grain slug an impressive 4,200 fps, churning up 1,570 fp of power. That's enough potential energy to lift 1,570 pounds a foot off the ground.
Rimfires are weak because of their ignition system. The priming compound lines the interior rim of the cartridge. It's ignited when the firing pin crushes that rim against the back rim of the barrel. In order to accomplish this crushing, the brass must be relatively thin, and that's what limits the allowable pressure. The .22 Win. Mag., because it's built on an lengthened .22 Long Rifle case with the same rim thickness/strength, is also held to 24,000 psi. The .17 HMR is allowed a peak of 25,600 psi, and the new .17 Win. Super Mag., build around a tougher case, can reportedly be pushed to 33,000 psi.
Historically, rimfires predated centerfires. In the mid-1800s, Smith & Wesson modified a percussion cap by putting the priming compound inside a lip or rim, then extended the sidewalls to hold a charge of powder capped with a bullet. Their First Model tip-up revolver was chambered for this rimfire round, the .22 short.
There followed dozens of rimfire cartridges such as the .44 Henry Flat and .56-56 Spencer, but all suffered from two shortcomings—they couldn't be easily reloaded and they couldn't withstand extreme pressures, so shooters invented the centerfire case.
Centerfire cartridges are built with thick, solid heads or "webbing" in their bases. A reloadable, self-contained primer is pushed into a hole in the center of this webbing, and it is held in place against extreme pressures of burning powder by the bolt faces of the rifles and shotguns that fire it.
Tougher cases, higher pressures, faster bullets, flatter trajectories and much higher impact energies make today's centerfire rifle cartridges the standard for big game hunting and all long-range shooting.